Rigidity results for overdetermined problems of p-Laplace equation with spatially dependent data

Let $p>1$ and $Ω\subset\mathbb{R}^n$ be a bounded smooth domain. We study the following overdetermined problem for the p-Laplacian: \begin{equation*} \left\{ \begin{array}{ll} -Δ_p u=f(x)&x\inΩ,\\ u=0&x\in\partialΩ,\\ \frac{\partial u}{\partialν}=g(x)&x\in\partialΩ, \end{array} \right. \end{equation